One of the biggest achievements in polytope theory was the complete characterization of \(f\) -vectors of simplicial polytopes, known as the \(g\) -theorem (for a precise statement see [1]}). In the early 70's Peter McMullen conjectured a set of necessary and sufficient conditions and less than a decade later Lou Billera and Carl Lee proved sufficiency, whereas Richard Stanley proved necessity. For an interesting survey about the history of this result we refer the reader to [2]}.
